We
live in a 3-Dimensional world. All objects have mass and take up space.
When we think of the space objects take up, we usually think in terms
of the objects length, width and height.

This introductory tutorial aims to demonstrate how computers can be
used to bridge the gap between the 2-Dimensional textbook world, most
of us are accustomed to, and the 3-Dimensional world we live in. It
will also demonstrate some of the functions of the Mage Software Program.
Many software packages now used in schools do not allow the user to
see objects as they really are in 3-Dimensions. The software package
you are about to use will present a more realistic view of an object;
you will be able to view an do measurements in 3-D space. You will
be able to rotate images, make them larger or smaller and make simple
calculations e.g., distance and angle measurements. And, one really
nice thing about this software is that it's in java. The original
program and files are not on your computer so you don't have to worry
if you make a mistake. Simply click the reload button on your browser
and start again.

To
make the activity easier you might want to open another window that
contains just the text, or you might want to make a hardcopy by printing
the text page.

If
you look at the screen for Tutorial I, you will see two points labeled
points A and point B.

Points
are considered dimensionless; they simply are used to represent positions
in space. Click on point A. At the lower left you will see the numbers
0,0,0 and another 0. The first three zeros represent the x,y,z coordinates
of point A. In class you are familiar with using x,y coordinates.
But since we are now dealing in 3-Dimensions we must also have a 3rd
axis. We will discuss this further in a future tutorial. The last
(or fourth) zero represents the distance between two consecutively
clicked points. Since you have not yet clicked a second point it reads
0. Now click on point B and see how the numbers change. The numbers
now read 4,0,0 and then 4. This means point B is 4 units to the right
along the x-axis. What do you think the fourth number represents?
It represents the distance between any two consecutively clicked points.
We will
explore this further toward the end of the lesson.

Click
on the 1-Dimension box at the right side of the screen. A line segment
will appear joining point A to point B. A line segment represents
an example of a 1-Dimensional figure. A true line segment has length
but has no width or height.

How
many units in length is line segment AB? ______________

Click
on the 2-Dimensions box. A square should become visible. The square
can be rotated in a clockwise motion by holding down the left cursor
button on your mouse and slowly moving the mouse or mouse ball. As
you move the square notice that the square is a 2-Dimensional object,
it has no thickness. If you wish to return the square to its original
position go to the VIEWS pulldown and click on View 1. Try it! If
you ever loose view of an object you can always return to the original
view by doing this or simply reloading the image. You can change the
size of the square by using the zoom buttons on the right side (to
the right of the MAGE graphics box).

Go
to the tools pulldown and select pick center. Click
on point B and rotate the object? Record what
has now changed _________________________________________________________
Repeat this for point A.

Click
off all objects on the screen by removing the X's on the boxes to
the right of the MAGE graphics box. Go to View 2 under Views. The
screen should still be blank. Click on 3-Dimensions. A
cube should appear. Try rotating the cube as you did the square.

Return
to View 1.

Explain
what happened to the cube? ______________________________________________________________

Go to View 3 and experiment with the zclip button. Move the zclip
button all the way to the right (800). Then slowly move it all the
way to the left. Explain what you think is the purpose of the z-clip
tool? Why z-clip and not x or y-clip?

Click
off everything so the screen is black. Set the view to View 2, and
click on the points box and 3-Dimensions. A grid of points in 3-D
space will appear within the cube. Click on any point.

Go
to the tools pulldown and click on markers. Click
on some points and see what effect it has. We will explore the the
measures pulldown in a later tutorial. To remove the the markers
use pulldown punch. Just be careful with punch because
it will --punch out-- anything you click on. Undo brings it back!

Using
the cube and points experiment again with the Pulldown pickcenter.
This is important because it gives you the point the object can be
rotated about. This will give a different perspective for each object
on the screen. Try it! Click on different vertices of the cube and
see what happens when you rotate it.

Try
now --Pulldown Draw line. Click on any two points.
A line will be drawn between any two points.At the lower left the
fourth number represents the distance between the two points. You
can continue this to form a triangle in space. After you have drawn
the object you are interested in return the pulldown to Tools
to prevent any more lines from being drawn.

Challenge
Question:

Draw
a right isosceles triangle using vertex points on the cube with sides
of 4 units. Measure the length of the hypotenuse of the triangle (longest
side). Can you check your results using the Pythagorean Theorem?